Simplify (mn^2)^3(m^2n^3)^4

(mn2)3(m2n3)4
Apply the product rule to mn2.
m3(n2)3(m2n3)4
Multiply the exponents in (n2)3.
Apply the power rule and multiply exponents, (am)n=amn.
m3n2⋅3(m2n3)4
Multiply 2 by 3.
m3n6(m2n3)4
m3n6(m2n3)4
Apply the product rule to m2n3.
m3n6((m2)4(n3)4)
Multiply the exponents in (m2)4.
Apply the power rule and multiply exponents, (am)n=amn.
m3n6(m2⋅4(n3)4)
Multiply 2 by 4.
m3n6(m8(n3)4)
m3n6(m8(n3)4)
Multiply m3 by m8 by adding the exponents.
Move m8.
m8m3n6(n3)4
Use the power rule aman=am+n to combine exponents.
m8+3n6(n3)4
m11n6(n3)4
m11n6(n3)4
Multiply the exponents in (n3)4.
Apply the power rule and multiply exponents, (am)n=amn.
m11n6n3⋅4
Multiply 3 by 4.
m11n6n12
m11n6n12
Multiply n6 by n12 by adding the exponents.
Move n12.
m11(n12n6)
Use the power rule aman=am+n to combine exponents.
m11n12+6